A digital image can be represented as a matrix of picture elements commonly referred to as pixels. Each pixel has a corresponding intensity value. For an eight bit “continuo us tone” gray scale image, that value can range from zero to two hundred fifty-five with zero representing white, two hundred fifty-five representing black, and the intermediate values representing varying levels of gray.
The digital image must be processed before it can be printed. A conventional black and white laser printer forms the image on a sheet of paper or other media by placing clusters of dots at selected locations on the sheet. Because printers cannot print continuous tones—whether it's the many shades of gray in a grayscale image or the millions of colors in a color photograph—digital images must be converted to halftones. This process is called halftoning or dithering.
Traditional halftoning methods change either the size of printed dots or the relative density of dots on the page. These two approaches are analogous to amplitude modulation (AM) or frequency modulation (FM) used in communications. For example, black and white continuous tone photographs can contain millions of shades of gray. When printed these shades of gray are converted to a pattern of black dots that simulates the continuous tones of the original image. Simply put, lighter shades of gray are composed of fewer or smaller black dots spaced further apart. Darker shades of gray contain more or larger black dots closely spaced.
With AM halftoning, the density of dot clusters, defined as the number of clusters of dots per unit area, is fixed. Tone rendition is achieved by varying the size of each dot. The most commonly used AM halftoning algorithm is clustered dot screening. Cluster dot screening has the advantages of low computational load, stable dot formation, and good resistance to such printer artifacts as dot gain and banding. Thus, it is widely used in laser printers where a single isolated dot may not develop stably. However, there are several drawbacks to AM halftoning. First, there is the well known tradeoff between the number of gray levels that can be rendered and the size of a screen period. Second, the regular dot placement in highlight regions may be very visible, and can cause Moiré artifacts when periodic patterns in the image are similar to the clustered dot frequency. This can be problematic when rendering images scanned from printed material.
With FM halftoning, the dot size is fixed and the tone rendition is achieved by varying the dot density. Commonly used FM halftoning algorithms include dispersed-dot screening, error diffusion, and search-based halftone methods such as direct binary search (DBS). Error diffusion is perhaps the most popular FM halftoning algorithm. Though it requires more computation as compared to screening, it is still very efficient. In general, FM halftoning achieves higher spatial resolution than AM halftoning and is free of Moiré artifacts. However, it can lack the print stability required for electro-photographic printing.
The characteristics of AM and FM methods are complementary to each other. However, traditional halftoning methods take an either/or approach. What is needed is a printing method and system that can take advantage of both methods while avoiding their drawbacks.